Endogenous price uncertainty and growth options.
The investment of Exhibit T16.1 is one of ten soybean processing plants that could be constructed in various Chinese provinces. A government panel will set the price of processed soybeans once production begins. The government panel will not commit to a price until production begins in at least one of the plants. As of today, the investment situation of each plant is identical to that in Exhibit T16.1.
a. Draw a decision tree depicting the choice between immediate investment in all ten plants and investment in a single plant with an option to expand investment in one year.
b. Calculate the NPV of investing today as if it were a now-or-never alternative.
c. Calculate the NPV (as of t = 0) of investing in a single plant (and hence revealing the government's price) and then waiting one year before considering further investment.
d. Decompose option value into intrinsic value and time value. Should investment be made all at once, sequentially, or not at all?
e. Suppose price will be either ¥70,000 or ¥30,000 with equal probability in one year. How does this increase in exogenous price uncertainty affect option value?
Exhibit T16.1
A proposed plant in China will process soybeans for the local (Chinese new yuan, or ¥) market. The sales price of a ton of processed soy will be determined by a government panel, and will be known with certainty in one year. The plant must decide whether to begin production today or in one year.
The following facts apply to the investment decision.
Initial investment I0 = ¥20,000,000 (rises at 10% per year)
Expected sales price per ton P0 = ¥50,000 per ton in perpetuity
Actual price P1 = either ¥40,000 or ¥60,000 with equal probability
Variable production cost VC = ¥40,000 per ton
Expected production Q = 500 tons per year forever
Tax rate TC = 0%
Discount rate i = 10%